The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Jayce R Getz - One of the best experts on this subject based on the ideXlab platform.
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a refined poisson Summation Formula for certain braverman kazhdan spaces
Science China-mathematics, 2021Co-Authors: Jayce R Getz, Baiying LiuAbstract:Braverman and Kazhdan (2000) introduced influential conjectures aimed at generalizing the Fourier transform and the Poisson Summation Formula. Their conjectures should imply that quite general Langlands L-functions have meromorphic continuations and functional equations as predicted by Langlands’ functoriality conjecture. As an evidence for their conjectures, Braverman and Kazhdan (2002) considered a setting related to the so-called doubling method in a later paper and proved the corresponding Poisson Summation Formula under restrictive assumptions on the functions involved. The connection between the two papers is made explicit in the work of Li (2018). In this paper, we consider a special case of the setting in Braverman and Kazhdan’s later paper and prove a refined Poisson Summation Formula that eliminates the restrictive assumptions of that paper. Along the way we provide analytic control on the Schwartz space we construct; this analytic control was conjectured to hold (in a slightly different setting) in the work of Braverman and Kazhdan (2002).
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a Summation Formula for the rankin selberg monoid and a nonabelian trace Formula
American Journal of Mathematics, 2020Co-Authors: Jayce R GetzAbstract:Let $F$ be a number field and let $\mathbb{A}_F$ be its ring of adeles. Let $B$ be a quaternion algebra over $F$ and let $\nu:B \to F$ be the reduced norm. Consider the reductive monoid $M$ over $F$ whose points in an $F$-algebra $R$ are given by \begin{align*} M(R):=\{(\gamma_1,\gamma_2) \in (B \otimes_F R)^{2}:\nu (\gamma_1)=\nu(\gamma_2)\}. \end{align*} Motivated by an influential conjecture of Braverman and Kazhdan we prove a Summation Formula analogous to the Poisson Summation Formula for certain spaces of functions on the monoid. As an application, we define new zeta integrals for the Rankin-Selberg $L$-function and prove their basic properties. We also use the Formula to prove a nonabelian twisted trace Formula, that is, a trace Formula whose spectral side is given in terms of automorphic representations of the unit group of $M$ that are isomorphic (up to a twist by a character) to their conjugates under a simple nonabelian Galois group.
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a Summation Formula for triples of quadratic spaces
Advances in Mathematics, 2019Co-Authors: Jayce R Getz, Baiying LiuAbstract:Abstract Let V 1 , V 2 , V 3 be a triple of even dimensional vector spaces over a number field F equipped with nondegenerate quadratic forms Q 1 , Q 2 , Q 3 , respectively. Let Y ⊂ ∏ i = 1 V i be the closed subscheme consisting of ( v 1 , v 2 , v 3 ) on which Q 1 ( v 1 ) = Q 2 ( v 2 ) = Q 3 ( v 3 ) . Motivated by conjectures of Braverman and Kazhdan and related work of Lafforgue, Ngo, and Sakellaridis we prove an analogue of the Poisson Summation Formula for certain functions on this space.
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a Summation Formula for triples of quadratic spaces
arXiv: Number Theory, 2017Co-Authors: Jayce R Getz, Baiying LiuAbstract:Let $V_1,V_2,V_3$ be a triple of even dimensional vector spaces over a number field $F$ equipped with nondegenerate quadratic forms $\mathcal{Q}_1,\mathcal{Q}_2,\mathcal{Q}_3$, respectively. Let \begin{align*} Y \subset \prod_{i=1}V_i \end{align*} be the closed subscheme consisting of $(v_1,v_2,v_3)$ on which $\mathcal{Q}_1(v_1)=\mathcal{Q}_2(v_2)=\mathcal{Q}_3(v_3)$. Motivated by conjectures of Braverman and Kazhdan and related work of Lafforgue, Ng\^o, and Sakellaridis we prove an analogue of the Poisson Summation Formula for certain functions on this space.
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a refined poisson Summation Formula for certain braverman kazhdan spaces
arXiv: Number Theory, 2017Co-Authors: Jayce R GetzAbstract:Braverman and Kazhdan introduced influential conjectures generalizing the Fourier transform and the Poisson Summation Formula. Their conjectures should imply that quite general Langlands $L$-functions have meromorphic continuations and functional equations as predicted by Langlands' functoriality conjecture. As evidence for their conjectures, Braverman and Kazhdan considered a setting related to the so-called doubling method in a later paper and proved the corresponding Poisson Summation Formula under restrictive assumptions on the functions involved. In this paper we consider a special case of the setting of the later paper, and prove a refined Poisson Summation Formula that eliminates the restrictive assumptions of loc. cit. Along the way we provide analytic control on the Schwartz space we construct; this analytic control was conjectured to hold (in a slightly different setting) in the work of Braverman and Kazhdan.
R L Stens - One of the best experts on this subject based on the ideXlab platform.
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the distance between the general poisson Summation Formula and that for bandlimited functions applications to quadrature Formulae
Applied and Computational Harmonic Analysis, 2017Co-Authors: Paul L Butzer, Gerhard Schmeisser, R L StensAbstract:Abstract The general Poisson Summation Formula of harmonic analysis and analytic number theory can be regarded as a quadrature Formula with remainder. The purpose of this investigation is to give estimates for this remainder based on the classical modulus of smoothness and on an appropriate metric for describing the distance of a function from a Bernstein space. Moreover, to be more flexible when measuring the smoothness of a function, we consider Riesz derivatives of fractional order. It will be shown that the use of the above metric in connection with fractional order derivatives leads to estimates for the remainder, which are best possible with respect to the order and the constants.
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the sampling theorem poisson s Summation Formula general parseval Formula reproducing kernel Formula and the paley wiener theorem for bandlimited signals their interconnections
Applicable Analysis, 2011Co-Authors: Paul L Butzer, Gerhard Schmeisser, J R Higgins, Paulo J S G Ferreira, R L StensAbstract:It is shown that the Whittaker–Kotel'nikov–Shannon sampling theorem of signal analysis, which plays the central role in this article, as well as (a particular case) of Poisson's Summation Formula, the general Parseval Formula and the reproducing kernel Formula, are all equivalent to one another in the case of bandlimited functions. Here equivalent is meant in the sense that each is a corollary of the other. Further, the sampling theorem is equivalent to the Valiron–Tschakaloff sampling Formula as well as to the Paley–Wiener theorem of Fourier analysis. An independent proof of the Valiron Formula is provided. Many of the equivalences mentioned are new results. Although the above theorems are equivalent amongst themselves, it turns out that not only the sampling theorem but also Poisson's Formula are in a certain sense the ‘strongest’ assertions of the six well-known, basic theorems under discussion.
Nobushige Kurokawa - One of the best experts on this subject based on the ideXlab platform.
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multiple zeta functions the double sine function and the signed double poisson Summation Formula
Compositio Mathematica, 2004Co-Authors: Shinya Koyama, Nobushige KurokawaAbstract:We construct multiple zeta functions as absolute tensor products of usual zeta functions. The Euler product expression is established for the most basic case $\zeta(s,\mathbf{F}_p)\otimes\zeta(s,\mathbf{F}_q)$ by using the signed double Poisson Summation Formula and the theory of the double sine function.
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multiple zeta functions the double sine function and the signed double poisson Summation Formula
Compositio Mathematica, 2004Co-Authors: Shinya Koyama, Nobushige KurokawaAbstract:We construct multiple zeta functions as absolute tensor products of usual zeta functions. The Euler product expression is established for the most basic case by using the signed double Poisson Summation Formula and the theory of the double sine function.
Baiying Liu - One of the best experts on this subject based on the ideXlab platform.
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a refined poisson Summation Formula for certain braverman kazhdan spaces
Science China-mathematics, 2021Co-Authors: Jayce R Getz, Baiying LiuAbstract:Braverman and Kazhdan (2000) introduced influential conjectures aimed at generalizing the Fourier transform and the Poisson Summation Formula. Their conjectures should imply that quite general Langlands L-functions have meromorphic continuations and functional equations as predicted by Langlands’ functoriality conjecture. As an evidence for their conjectures, Braverman and Kazhdan (2002) considered a setting related to the so-called doubling method in a later paper and proved the corresponding Poisson Summation Formula under restrictive assumptions on the functions involved. The connection between the two papers is made explicit in the work of Li (2018). In this paper, we consider a special case of the setting in Braverman and Kazhdan’s later paper and prove a refined Poisson Summation Formula that eliminates the restrictive assumptions of that paper. Along the way we provide analytic control on the Schwartz space we construct; this analytic control was conjectured to hold (in a slightly different setting) in the work of Braverman and Kazhdan (2002).
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a Summation Formula for triples of quadratic spaces
Advances in Mathematics, 2019Co-Authors: Jayce R Getz, Baiying LiuAbstract:Abstract Let V 1 , V 2 , V 3 be a triple of even dimensional vector spaces over a number field F equipped with nondegenerate quadratic forms Q 1 , Q 2 , Q 3 , respectively. Let Y ⊂ ∏ i = 1 V i be the closed subscheme consisting of ( v 1 , v 2 , v 3 ) on which Q 1 ( v 1 ) = Q 2 ( v 2 ) = Q 3 ( v 3 ) . Motivated by conjectures of Braverman and Kazhdan and related work of Lafforgue, Ngo, and Sakellaridis we prove an analogue of the Poisson Summation Formula for certain functions on this space.
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a Summation Formula for triples of quadratic spaces
arXiv: Number Theory, 2017Co-Authors: Jayce R Getz, Baiying LiuAbstract:Let $V_1,V_2,V_3$ be a triple of even dimensional vector spaces over a number field $F$ equipped with nondegenerate quadratic forms $\mathcal{Q}_1,\mathcal{Q}_2,\mathcal{Q}_3$, respectively. Let \begin{align*} Y \subset \prod_{i=1}V_i \end{align*} be the closed subscheme consisting of $(v_1,v_2,v_3)$ on which $\mathcal{Q}_1(v_1)=\mathcal{Q}_2(v_2)=\mathcal{Q}_3(v_3)$. Motivated by conjectures of Braverman and Kazhdan and related work of Lafforgue, Ng\^o, and Sakellaridis we prove an analogue of the Poisson Summation Formula for certain functions on this space.
Dumitru Popa - One of the best experts on this subject based on the ideXlab platform.
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a multiple abel Summation Formula and asymptotic evaluations for multiple sums
International Journal of Number Theory, 2017Co-Authors: Magdalena Bănescu, Dumitru PopaAbstract:In this paper, we prove a multiple Abel Summation Formula and give some applications of this Formula. We use these evaluations in tandem with some recent results to obtain various asymptotic evalua...
